The paychecks of Port Authority cops are soaring higher than a 747 — because agency officials decided they’d rather pay huge amounts of overtime than appoint new sergeants and lieutenants, The Post has learned.

“This is an agency that puts its lieutenants on overtime to supervise cops — to make sure they’re really earning their straight time,’’ a source said yesterday.

“They think it’s cheaper.’’

Overtime for sergeants and lieutenants surged more than 80 percent in the first quarter of 2012, compared to the same period in the previous year.

The PA paid its police $12.3 million overtime in the first three months of this year, as opposed to $6.8 million in 2011.

That represents 189,912 hours compared to 112,251 hours.

This despite the PAPD insisting it put into effect strong protocols last year to make sure that nothing like this would happen.

These included regulations that unit supervisors strictly monitor overtime requests to assure they’re necessary. And more documentation is being insisted on to prove the need for assigned OT.

Most of the overtime money is going to the agency’s 117 sergeants and 67 lieutenants.

In late January 2009, the PA had 141 sergeants and 79 lieutenants.

The number of lower- ranking cops they supervise now is 1,332, compared to 1,452 three years ago.

“The department today is woefully deficient in sergeants and lieutenants,’’ the source said.

The problem is not new, the source said, adding, “The department has always preferred to pay overtime because they think it’s cheaper.’’

The last officers promoted were 14 sergeants raised to lieutenant last July.

Captains and higher-ranking cops do not make overtime.

Top officials won’t say if it’s true that they’d rather pay overtime than promote patrol officers to higher-level positions.

But they note that at least as of now, it’s basically a moot point.

That’s because promotion exams are tied up in litigation over alleged discrimination and investigations into suspicion of cheating.

A captain was recently fired after he was spotted photographing questions on the lieutenants exam and e-mailing them.

Three other officials also lost their jobs as a result of the probe.

But it’s not clear whether any of the answers were actually passed on to candidates.

The good news is that overtime in the rest of the Port Authority is down by about 16 percent for the first three months of the year — a drop of more than 65,000 overtime hours.

But officials haven’t yet figured out whether that will make up for the extra police overtime.

The union representing Port Authority cops declined to comment.

PA salaries and overtime come mainly from fees and tolls charged at its facilities.